Reshetnyak S Theory Of Subharmonic Metrics
DOWNLOAD
Download Reshetnyak S Theory Of Subharmonic Metrics PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Reshetnyak S Theory Of Subharmonic Metrics book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Reshetnyak S Theory Of Subharmonic Metrics
DOWNLOAD
Author : François Fillastre
language : en
Publisher: Springer Nature
Release Date : 2023-09-15
Reshetnyak S Theory Of Subharmonic Metrics written by François Fillastre and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-15 with Mathematics categories.
Despite the fundamental role played by Reshetnyak's work in the theory of surfaces of bounded integral curvature, the proofs of his results were only available in his original articles, written in Russian and often hard to find. This situation used to be a serious problem for experts in the field. This book provides English translations of the full set of Reshetnyak's articles on the subject. Together with the companion articles, this book provides an accessible and comprehensive reference for the subject. In turn, this book should concern any researcher (confirmed or not) interested in, or active in, the field of bounded integral curvature surfaces, or more generally interested in surface geometry and geometric analysis. Due to the analytic nature of Reshetnyak's approach, it appears that his articles are very accessible for a modern audience, comparing to the works using a more synthetic approach. These articles of Reshetnyak concern more precisely the work carried by the author following the completion of his PhD thesis, under the supervision of A.D. Alexandrov. Over the period from the 1940’s to the 1960’s, the Leningrad School of Geometry, developed a theory of the metric geometry of surfaces, similar to the classical theory of Riemannian surfaces, but with lower regularity, allowing greater flexibility. Let us mention A.D. Alexandrov, Y.D. Burago and V.A. Zalgaller. The types of surfaces studied by this school are now known as surfaces of bounded curvature. Particular cases are that of surfaces with curvature bounded from above or below, the study of which gained special attention after the works of M. Gromov and G. Perelman. Nowadays, these concepts have been generalized to higher dimensions, to graphs, and so on, and the study of metrics of weak regularity remains an active and challenging field. Reshetnyak developed an alternative and analytic approach to surfaces of bounded integral curvature. The underlying idea is based on the theorem of Gauss which states that every Riemannian surface is locally conformal to Euclidean space. Reshetnyak thus studied generalized metrics which are locally conformal to the Euclidean metric with conformal factor given by the logarithm of the difference between two subharmonic functions on the plane. Reshetnyak's condition appears to provide the correct regularity required to generalize classical concepts such as measure of curvature, integral geodesic curvature for curves, and so on, and in turn, to recover surfaces of bounded curvature. Chapter-No.7, Chapter-No.8, Chapter-No.12 and Chapter-No.13 are available open access under Creative Commons Attribution-NonCommercial 4.0 International License via link.springer.com.
Geometry Iv
DOWNLOAD
Author : Yu.G. Reshetnyak
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Geometry Iv written by Yu.G. Reshetnyak and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
The book contains a survey of research on non-regular Riemannian geome try, carried out mainly by Soviet authors. The beginning of this direction oc curred in the works of A. D. Aleksandrov on the intrinsic geometry of convex surfaces. For an arbitrary surface F, as is known, all those concepts that can be defined and facts that can be established by measuring the lengths of curves on the surface relate to intrinsic geometry. In the case considered in differential is defined by specifying its first geometry the intrinsic geometry of a surface fundamental form. If the surface F is non-regular, then instead of this form it is convenient to use the metric PF' defined as follows. For arbitrary points X, Y E F, PF(X, Y) is the greatest lower bound of the lengths of curves on the surface F joining the points X and Y. Specification of the metric PF uniquely determines the lengths of curves on the surface, and hence its intrinsic geometry. According to what we have said, the main object of research then appears as a metric space such that any two points of it can be joined by a curve of finite length, and the distance between them is equal to the greatest lower bound of the lengths of such curves. Spaces satisfying this condition are called spaces with intrinsic metric. Next we introduce metric spaces with intrinsic metric satisfying in one form or another the condition that the curvature is bounded.
St Petersburg Mathematical Journal
DOWNLOAD
Author :
language : en
Publisher:
Release Date : 1999
St Petersburg Mathematical Journal written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Algebra categories.
Geometry Iii
DOWNLOAD
Author : Yu.D. Burago
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Geometry Iii written by Yu.D. Burago and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
The original version of this article was written more than fiveyears ago with S. Z. Shefel',a profound and original mathematician who died in 1984. Sincethen the geometry of surfaces has continued to be enriched with ideas and results. This has required changes and additions, but has not influenced the character of the article, the design ofwhich originated with Shefel'. Without knowing to what extent Shefel' would have approved the changes, I should nevertheless like to dedicate this article to his memory. (Yu. D. Burago) We are trying to state the qualitative questions of the theory of surfaces in Euclidean spaces in the form in which they appear to the authors at present. This description does not entirely correspond to the historical development of the subject. The theory of surfaces was developed in the first place mainly as the 3 theory of surfaces in three-dimensional Euclidean space E ; however, it makes sense to begin by considering surfaces F in Euclidean spaces of any dimension n~ 3. This approach enables us, in particular, to put in a new light some 3 unsolved problems of this developed (and in the case of surfaces in E fairly complete) theory, and in many cases to refer to the connections with the present stage ofdevelopment of the theory of multidimensional submanifolds. The leading question of the article is the problem of the connection between classes of metrics and classes of surfaces in En.
Harmonic Quasiconformal Mappings And Hyperbolic Type Metrics
DOWNLOAD
Author : Vesna Todorčević
language : en
Publisher: Springer
Release Date : 2019-07-24
Harmonic Quasiconformal Mappings And Hyperbolic Type Metrics written by Vesna Todorčević and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-24 with Mathematics categories.
The book presents a research area in geometric function theory concerned with harmonic quasiconformal mappings and hyperbolic type metrics defined on planar and multidimensional domains. The classes of quasiconformal and quasiregular mappings are well established areas of study in this field as these classes are natural and fruitful generalizations of the class of analytic functions in the planar case. The book contains many concrete examples, as well as detailed proofs and explanations of motivations behind given results, gradually bringing the reader to the forefront of current research in the area. This monograph was written for a wide readership from graduate students of mathematical analysis to researchers working in this or related areas of mathematics who want to learn the tools or work on open problems listed in various parts of the book.
Quasiconformal Space Mappings
DOWNLOAD
Author : Matti Vuorinen
language : en
Publisher: Springer
Release Date : 2006-11-14
Quasiconformal Space Mappings written by Matti Vuorinen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
This volume is a collection of surveys on function theory in euclidean n-dimensional spaces centered around the theme of quasiconformal space mappings. These surveys cover or are related to several topics including inequalities for conformal invariants and extremal length, distortion theorems, L(p)-theory of quasiconformal maps, nonlinear potential theory, variational calculus, value distribution theory of quasiregular maps, topological properties of discrete open mappings, the action of quasiconformal maps in special classes of domains, and global injectivity theorems. The present volume is the first collection of surveys on Quasiconformal Space Mappings since the origin of the theory in 1960 and this collection provides in compact form access to a wide spectrum of recent results due to well-known specialists. CONTENTS: G.D. Anderson, M.K. Vamanamurthy, M. Vuorinen: Conformal invariants, quasiconformal maps and special functions.- F.W. Gehring: Topics in quasiconformal mappings.- T.Iwaniec: L(p)-theory of quasiregular mappings.- O. Martio: Partial differential equations and quasiregular mappings.- Yu.G. Reshetnyak: On functional classes invariant relative to homothetics.- S. Rickman: Picard's theorem and defect relation for quasiconformal mappings.- U. Srebro: Topological properties of quasiregular mappings.- J. V{is{l{: Domains and maps.- V.A. Zorich: The global homeomorphism theorem for space quasiconformal mappings, its development and related open problems.
Two Dimensional Manifolds Of Bounded Curvature
DOWNLOAD
Author : Aleksandr Danilovich Aleksandrov
language : en
Publisher: American Mathematical Soc.
Release Date : 1967
Two Dimensional Manifolds Of Bounded Curvature written by Aleksandr Danilovich Aleksandrov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with Mathematics categories.
Proceedings and papers about in which the foundation of the intrinsic geometry of nonregular surfaces is developed.
Mathematical Reviews
DOWNLOAD
Author :
language : en
Publisher:
Release Date : 2003
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
Siberian Advances In Mathematics
DOWNLOAD
Author :
language : en
Publisher:
Release Date : 2001
Siberian Advances In Mathematics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
Handbook Of Complex Analysis
DOWNLOAD
Author : Reiner Kuhnau
language : en
Publisher: Elsevier
Release Date : 2004-12-09
Handbook Of Complex Analysis written by Reiner Kuhnau and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-12-09 with Mathematics categories.
Geometric Function Theory is that part of Complex Analysis which covers the theory of conformal and quasiconformal mappings. Beginning with the classical Riemann mapping theorem, there is a lot of existence theorems for canonical conformal mappings. On the other side there is an extensive theory of qualitative properties of conformal and quasiconformal mappings, concerning mainly a prior estimates, so called distortion theorems (including the Bieberbach conjecture with the proof of the Branges). Here a starting point was the classical Scharz lemma, and then Koebe's distortion theorem. There are several connections to mathematical physics, because of the relations to potential theory (in the plane). The Handbook of Geometric Function Theory contains also an article about constructive methods and further a Bibliography including applications eg: to electroxtatic problems, heat conduction, potential flows (in the plane). · A collection of independent survey articles in the field of GeometricFunction Theory · Existence theorems and qualitative properties of conformal and quasiconformal mappings · A bibliography, including many hints to applications in electrostatics, heat conduction, potential flows (in the plane).